feat(newton): first newton solver implementation

tests/operators/prepared_pressure_force.cpp

@@ -3,6 +3,7 @@
 #include <cmath>
 #include <limits>
 #include <memory>
+#include <stdexcept>
 
 #include <catch2/catch_test_macros.hpp>
 #include <mfem.hpp>
@@ -51,6 +52,26 @@ namespace prepared_pressure_force_test_utils {
         }
     };
 
+    [[nodiscard]] mfem::Vector make_affine_displacement(
+        const mean_field::fem::FEM &f,
+        const double scale
+    ) {
+        mfem::ParGridFunction field(f.displacementFes.get());
+        mfem::VectorFunctionCoefficient coefficient(
+            f.mesh->Dimension(), [scale](const mfem::Vector &position, mfem::Vector &value) {
+                value.SetSize(position.Size());
+                for (int dimension = 0; dimension < position.Size(); ++dimension) {
+                    value(dimension) = scale * position(dimension);
+                }
+            }
+        );
+        field.ProjectCoefficient(coefficient);
+
+        mfem::Vector result;
+        field.GetTrueDofs(result);
+        return result;
+    }
+
     [[nodiscard]]
     mfem::Vector make_positive_enthalpy_true(
         const mean_field::fem::FEM &f,
@@ -265,6 +286,97 @@ TEST_CASE(
     );
 }
 
+TEST_CASE(
+    "Prepared Pressure Force Reports Expected EOS Rejections Without Unwinding",
+    tags::barotrope &tags::pressure &tags::prepared &tags::unit
+) {
+    mean_field::utils::Args args = test_utils::setup_args();
+    mean_field::fem::FEM f       = mean_field::fem::setup_fem(args.mesh_file, args, 0);
+    REQUIRE(f.okay());
+
+    const prepared_pressure_force_test_utils::Maps maps(f);
+    const mean_field::eos::Polytrope equationOfState(3.0, 0.25);
+    mean_field::operators::PreparedPressureForceOperator preparedOperator(f, *f.domainMapperStateless, equationOfState);
+
+    mfem::Vector enthalpy(maps.enthalpy.reduced_size());
+    mfem::Vector displacement(maps.displacement.reduced_size());
+    enthalpy          = -1.0;
+    displacement      = 0.0;
+    auto dependencies = prepared_pressure_force_test_utils::make_dependencies();
+
+    const auto outsideDomain =
+        preparedOperator.TryPrepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies);
+    REQUIRE_FALSE(outsideDomain.has_value());
+    CHECK(
+        outsideDomain.error().reason ==
+        mean_field::operators::PressureForcePreparationRejectionReason::equation_of_state
+    );
+    CHECK(outsideDomain.error().equationOfStateCode == mean_field::eos::EvaluationErrorCode::outside_domain);
+    CHECK_FALSE(preparedOperator.IsPrepared());
+    try {
+        (void)preparedOperator.Prepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies);
+        FAIL("The compatibility Prepare overload accepted an out-of-domain EOS input.");
+    } catch (const mean_field::eos::EvaluationError &error) {
+        CHECK(error.code() == mean_field::eos::EvaluationErrorCode::outside_domain);
+    }
+
+    enthalpy = std::numeric_limits<double>::max();
+    ++dependencies.enthalpy.revision;
+    const auto rejected =
+        preparedOperator.TryPrepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies);
+    REQUIRE_FALSE(rejected.has_value());
+    CHECK(rejected.error().reason == mean_field::operators::PressureForcePreparationRejectionReason::equation_of_state);
+    CHECK(rejected.error().equationOfStateCode == mean_field::eos::EvaluationErrorCode::nonfinite_result);
+    CHECK_FALSE(preparedOperator.IsPrepared());
+    CHECK_THROWS_AS(
+        preparedOperator.Prepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies),
+        mean_field::eos::EvaluationError
+    );
+
+    enthalpy = 1.0;
+    ++dependencies.enthalpy.revision;
+    const auto accepted =
+        preparedOperator.TryPrepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies);
+    REQUIRE(accepted.has_value());
+    CHECK(preparedOperator.IsPrepared());
+}
+
+TEST_CASE(
+    "Prepared Pressure Force Reports Invalid Candidate Geometry Without Unwinding",
+    tags::barotrope &tags::pressure &tags::prepared &tags::geometry &tags::unit
+) {
+    mean_field::utils::Args args = test_utils::setup_args();
+    mean_field::fem::FEM f       = mean_field::fem::setup_fem(args.mesh_file, args, 0);
+    REQUIRE(f.okay());
+
+    const prepared_pressure_force_test_utils::Maps maps(f);
+    const mean_field::eos::Polytrope equationOfState(3.0, 0.25);
+    mean_field::operators::PreparedPressureForceOperator preparedOperator(f, *f.domainMapperStateless, equationOfState);
+
+    mfem::Vector enthalpy(maps.enthalpy.reduced_size());
+    enthalpy = 1.0;
+    mfem::Vector displacement =
+        maps.displacement.gather(prepared_pressure_force_test_utils::make_affine_displacement(f, -2.0));
+    auto dependencies = prepared_pressure_force_test_utils::make_dependencies();
+
+    const auto rejected =
+        preparedOperator.TryPrepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies);
+    REQUIRE_FALSE(rejected.has_value());
+    CHECK(rejected.error().reason == mean_field::operators::PressureForcePreparationRejectionReason::invalid_mapping);
+    CHECK(rejected.error().mappingStatus == mean_field::mapping::MappingStatus::non_positive_determinant);
+    CHECK_FALSE(preparedOperator.IsPrepared());
+    CHECK_THROWS_AS(
+        preparedOperator.Prepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies), std::domain_error
+    );
+
+    displacement = 0.0;
+    ++dependencies.displacement.revision;
+    const auto accepted =
+        preparedOperator.TryPrepare({.enthalpy = enthalpy, .displacement = displacement}, dependencies);
+    REQUIRE(accepted.has_value());
+    CHECK(preparedOperator.IsPrepared());
+}
+
 TEST_CASE(
     "Prepared Pressure Force Jacobian Matches Full Stateless Columns "
     "Through FieldDof Restriction",